One way to define a bad game might be that even a comparatively forgiving player finds him/herself constantly going "why didn't they fix this?" or "what reason could they possibly have had for making this design decision?" or "this game isn't even finished..."
There are a lot of ways to screw games up. Like:
Contradicting the story with the gameplay - for instance, you play an allegedly nice and kindly guy who kills every living thing that opposes him, be it human, animal or alien...
Failing to make the game fun - making the player do a variety of pointless things just to rack up the "70 hours of gameplay" or whatever they choose to put on the box. Huge mistake, I'm sure just about anyone would rather pay for a short, fun game that they'd be likely to play and enjoy several more times, than for a game they get sick of long before they get anywhere near finishing it...
Offending the player - this may be difficult with some players, but take for instance those games that REALLY rub it in when you die or otherwise lose the game, THEN kick you back to the beginning of a long level full of very difficult challenges that you've already overcome. Red Ninja did this; besides its nigh-on worthless controls and camera, the game features difficult combat, a number of extra tough, extra strong enemies to fight, far too few checkpoints and no quicksave or anything like that, as well as instant death from a variety of things; jumping puzzles, dodgy wallrunning and confusing level design, mainly. Plus the bosses are viciously difficult, often include some gimmick like "kill him before he reaches your friend" or "avoid his attacks until he uses the one that lets you damage him with a strangling move", and if you die you have to start over from the beginning of the fight again. That wouldn't be too bad, if only they didn't have about a hundred times your health, far better moves and the aforementioned gimmick strengths (read that as "invulnerabilities) and weakness(es, as if you're ever that lucky)...
...Come to think of it, a bad game is Red Ninja.
/rant